Question

How do you solve the inequality: `x^2 + 7x + 10 > 0`?

Answer 1

Solve quadratic inequality: `y = x^2 + 7x + 10 > 0`(1)

Explanation:

First solve `y = x^2 + 7x + 10 = 0` to get the 2 real roots.
Find 2 number p and q knowing sun (-b = -7) and product (c = 10).
Both p and q are negative (Rule of signs)
Factor pairs of (10)--> (-1, -10)(-2, -5). This sum is (-7 = -b). Therefor, the 2 real roots are -2 and - 5.
Solve the inequality (1) by the algebraic method. Outside the interval (-5, -2), f(x) > 0.
Answer by open intervals: (-infinity, -5) and (-2, infinity).
Since a > 0 the parabola opens upward. Inside the interval f(x) has the opposite sign of a, and f(x) has the same sign as a, f(x) > 0, out side the interval.
graph{x^2 + 7x + 10 [-10, 10, -5, 5]}